Vehicle Linear and Rotational Acceleration, Velocity and Displacement During Staged Rollover Collisions

2007-01-0732 Vehicle Linear and Rotational Acceleration, Velocity and Displacement during Staged Rollover Collisions

Orion P. Keifer, Wesley C. Richardson, Peter D. Layson, Bradley C. Reckamp, and Thomas C. Heilmann Applications Engineering Group, Inc.

ABSTRACT vehicles and nearly any test surface. The test vehicles were instrumented to determine both the Four full scale vehicle rollover tests, about the roll angular and linear acceleration, from which the axis (X-axis), were staged using a sled attached to angular and linear velocities and displacements a large truck. Each vehicle was fitted with a nine- could be determined. accelerometer array that approximated the center of gravity and two single axis accelerometers METHODOLOGY attached to the roof adjacent to the A-pillar/roof junction. The acceleration data was retrieved for Vehicles three tests; however, the data recorder malfunctioned on the remaining test. Data was The test vehicles for the testing included the collected at 1000 hertz and processed to determine following: the linear and rotational acceleration with respect to each of the three vehicle coordinate axes. Vehicle VIN Color Rollover video and scene data were also collected 1989 Buick 1G4CU54C0K1668358 Gold to correlate vehicle rollover motion with the Park Avenue Ultra accelerometer data. 1994 Oldsmobile 1G3HN52L9R4818549 Blue 88 Royale INTRODUCTION 1997 Pontiac 1G2NE52TXVC866133 White Grand Am Full scale rollover tests have been conducted over 1995 Mercury 3MASM10J9SR647656 Green many years. Much of the work has been Tracer performed using various test sleds. One of the Table 1. Vehicle data. most common is the Federal Motor Vehicle Safety Standard (FMVSS) 208 sled test, which is Vehicle Mass kg Length m Width m SSF* conducted in accordance with SAE J2114, for Buick 1462 5.00 1.83 1.44 example the Malibu tests (Orlowski, et al., 1985 Oldsmobile 1573 5.08 1.88 1.36 and Bahling, et al., 1990). The FMVSS 208 test sled ramp angle is 23º and the test is conducted Pontiac 1307 4.75 1.73 1.34 using an initial speed of 30 miles per hour. The Mercury 1095 4.34 1.70 1.37 sled is decelerated to a stop in less than 3 feet and Table 2. Vehicle data. * Static Stability Factor (half the track a deceleration rate of at least 20 g’s for a width divided by the center of gravity height). minimum of 0.04 seconds. Sled The test procedure used for this work has a sled angle of 34º and a deceleration rate of The sled was manufactured using a utility trailer approximately 0.6 g’s; however, the tests required frame set side-ways. Two fixed axles were minimal apparatus that can be used for most attached to the frame. Two ramps, one for the front and one for the rear axles, were welded in place at an angle of approximately 34º (Figure 1). center accelerometer and the two channels for The designed ramp angle was determined using a each of the three legs. first order approximation, neglecting suspension compliance, such that all test vehicles would: first, be stable while the sled was stopped or accelerating and second, roll off the sled when the pusher truck was heavily braking. Rollover occurs when the line of action of the force through the center of gravity of the vehicle is forward of the front lip of the sled. That occurs when the sum of three angles exceed 90°. The three angles are the sled ramp angle, the angle formed by the ground and a line passing through the vehicle center of gravity, with the apex at the center of the Figure 2. Diagram of the sled angles. outboard tire, which is calculated using the Static Three channels of a 2g triaxial accelerometer, Stability Factor (SSF) and the friction angle due installed on the floor near the center of gravity, to braking, shown on Figure 2. In this first order were monitored. Two single axial 50g approximation, the braking deceleration required accelerometers were placed near the right and left to cause the vehicle to roll was calcuated between A-pillar roof intersection. The position and 0.35 and 0.4 g’s, depending on the test vehicle. orientation, with respect to the vehicle coordinate The front bumper of the pusher truck was axis varied from vehicle to vehicle, but in general removed and brackets fabricated for this test were were oriented mostly vertically with a forward and mounted on the frame members. The sled was outboard component as dictated by the interior then pinned to the frame brackets with two contour at the A-pillar to roof contour inside the transverse pins, one for each side. vehicle.

Additionally, one data collection channel monitored a microphone, used for video to data collection synchronization.

Figure 3 shows a photograph of the test equipment installed in one of the test vehicles.

Figure 1. Photograph of the sled arrangement.

Instrumentation

A computer system was assembled to collect data, the details of which are in Appendix A. All data was collected with 12 bit resolution. Figure 3. Photograph of the nine-accelerometer array frame inside a test vehicle. The monitored accelerometers included a nine- accelerometer array, as proposed by Padgaonkar, Video et al. (1975) and Mital and King (1979), including three mutually perpendicular channels on the Video cameras were used to capture the roll-over from the side and from the front. Cones were placed on the test surface and measured as reference points for photogrammetric processing. The positions of the cones and video cameras were surveyed.

TEST PROCEDURE

The truck and sled were lined up on the test track and the vehicle was placed on the test sled. A balloon was popped adjacent to the test vehicle to provide synchronization between the data collection system and the video cameras. The video cameras captured the frame during which Figure 4. Buick the balloons popped and the data recorder captured the sound on the channel which monitored the microphone.

The truck was accelerated and the speed of the truck was monitored with a Stalker radar gun. The truck steering was adequate to maintain a straight line of travel. As the truck crossed a predetermined line marked by cones, the driver locked up the brakes, causing the test vehicle to roll off the sled. When the vehicle came to final rest, a second balloon was popped adjacent to the final rest position of the vehicle, to synchronize Figure 5. Oldsmobile the video with the data collection system. The data was downloaded from the data collection system via an Ethernet connection. The vehicle was photographed and marks on the pavement were documented.

RESULTS The roll data and distance traveled is summarized in Table 3.

Buick Oldsmobile Pontiac Mercury Lead direction Driver Passenger Driver Driver Initial Vel. (kph) 55.5 54.7 56.3 56.3 Figure 6. Pontiac Rolls* 2 2 4 1/4 1 1/2 Yaw (final rest) 10ºCW 70º CCW 35ºCW 20ºCW Distance to Rest (m) 26.1 23.5 39.6 28.1 Drag factor 0.50 0.54 0.34 0.48 Table 3. Roll and distance data for the tested vehicles. * Including the initial 34°.

Figures 4 through 7 show the damage received by the four vehicles during the rollover.

Figure 7. Mercury Additional post-rollover photographs of the Recommended Practice J211-1 (SAE J211-1) for vehicles are enclosed in Appendix B. As defined Channel Frequency Classes CFC-60 and CFC- by the authors, the roll of the vehicle began when 180. It should be noted that the filtering frequency the following side (upper ramp) tires first lifted was the highest justified by the response of the off the ramp. The position of the test vehicle at accelerometers used. While it is less than the tire lift-off was determined from video analysis CFC-180 recommended for integration for speed and photogrammetry. The final rest position of and position, it exceeds the recommendation of the geometric center of the vehicle was CFC-60 for vehicle structural accelerations. determined by survey and checked using video Rotational acceleration was calculated using the analysis and photogrammetry. The initial speed formulation of Mital and King (1979). The of the test vehicle was determined by the peak rotational vectors were then transformed into the speed from Stalker data. Of note, the peak speed standard SAE vehicle coordinate system (positive was used from the Stalker data graphs for the x direction, forward, positive y direction to right Buick, Pontiac and Mercury. The graph for the and positive z direction, down). The transformed Oldsmobile was not retained and therefore, the rotational acceleration data showed a bias both recorded peak speed was used. before the roll started and after final rest, when the values should have been zero. Linear correction to the data during the period of rollover motion was made to the rotational acceleration, which was then numerically integrated to determine the rotational velocity. A similar bias was seen in the angular velocity data, which was removed by a linear correction. The corrected angular velocity data was numerically integrated a second time for the rotational displacement. The calculated rotational displacement was compared to visual Figure 8. Stalker data. Left peak is for the Buick, middle observation at final rest to determine the error, peak for the Pontiac and the right peak is for the thus checking the initial accelerometer accuracy as Mercury. well as the required corrections and vector transformations. The distance traveled during the roll and the Calculated Roll Visual Roll average drag factor was calculated and presented Vehicle Percent Error in Table 3. Displacement Displacement Buick 665º 686º 3% Accelerometer Data Processing Oldsmobile 785º 686º 14% Pontiac 1490º 1496º 0% Video and numerical data from the data collection system were first synchronized, and then the data Table 4. Calculated roll displacement (double integration of of interest (approximately 15 seconds worth) was the rotational acceleration data) compared to the extracted. visual roll displacement.

The raw accelerometer data was processed by Table 4 compares the rotational displacement converting the voltage to multiples of the calculated by the double integration to the visual acceleration of gravity (g’s) and applying displacement. As can be seen, the error after the corrections based on the calibration data for each subtraction of accelerometer data and subsequent accelerometer channel. The accelerometer offset double integration is acceptably small for the was calculated and removed, based on the initial Buick and the Pontiac. The integration data for rest position where all acceleration data would the Oldsmobile suggests that the actual rotational correspond to the gravity vector. The data was acceleration is somewhat higher than recorded. then filtered using a digital four-pole Butterworth The rotational acceleration data for the Buick, filter at 100 Hz. The filter used was SimFil, Oldsmobile and Pontiac are presented in Figure 9. obtained from the NHTSA website, which meets Note that the horizontal axes are matched for the the filtering requirements of SAE Surface Vehicle three vehicles for comparison. Darker backround determined. These projections were subtracted indicates ground contact of the vehicle, based on from the accelerometer data. video analysis. Larger graphs are presented in Angular Acceleration Appendix C. 15 0 10 0

Angular Acceleration 2 0 15 0 1 1001 2001 3001 4001 5001 6001 X -50rad/s 10 0 -100 50 -150 2 0 X -200 1 1001 2001 3001 4001 5001 6001 Y ms -50rad/s Z -100

-150 Buick -200 Angular Acceleration ms 10 0 Buick 50 0 Angular Acceleration 1 1001 2001 3001 4001 5001 6001 15 0 X

rad/s2 -50 10 0

-100 50 X 0 Y -150

rad/s2 1 1001 2001 3001 4001 5001 6001 ms -50 Z -100 Oldsmobile -150 Angular Acceleration ms 15 0 Oldsmobile 10 0 50 Angular Acceleration 2 15 0 0 X rad/s 1 1001 2001 3001 4001 5001 6001 10 0 -50

50 -100 2 X 0 Y -150 rad/s 1 1001 2001 3001 4001 5001 6001 ms -50 Z -100 Pontiac

-150 ms Figure 10. Rotational acceleration for X-axis for the three Pontiac vehicles. Larger graphs are presented in Figure 9. Triaxial angular acceleration for all three vehicles. Appendix C. Larger graphs are presented in Appendix C. Angular Velocity 2 1 The X-axis rotational acceleration for the three 0 -1 1 1001 2001 3001 4001 5001 6001 -2 X vehicles is presented in Figure 10 and the X-axis rad/s -3 -4 rotational velocity for the three vehicles is -5 -6 -7 presented in Figure 11. Note the darker ms background indicates that the vehicle is touching Buick Angular Velocity the ground and the light background, the vehicle is 9 8 7 fully in the air, as determined by video 6 5 analysis/photogrammetry. Clearly the ground 4 3 X rad/s 2 contacts can be seen as linear and rotational 1 0 -1 1 1001 2001 3001 4001 5001 6001 acceleration spikes. -2 ms Oldsmobile The linear acceleration was taken from the filtered Angular Velocity 0 1 1001 2001 3001 4001 5001 6001 acceleration data from the center tri-axial -2 accelerometer and transformed into the vehicle -4 -6

rad/s X coordinate axis. The linear acceleration is, -8 however, confounded by the inclusion of gravity -10 -12 in the measured acceleration. To remove the ms effect of gravity, the position of the vehicle with Pontiac respect to the ground reference was needed. Key Figure 11. Angular velocity for all three vehicles. Larger frames of the synchronized videos were used to graphs are presented in Appendix C. position a three dimensional computer model of The three axis linear acceleration data is presented the vehicle, with straight line motion calculated for the three vehicles in Figure 12. The between key frames. The orientations of the magnitude (vector sum) acceleration is presented model, every thousandth of a second, were in Figure 13. calculated and the projection of the vehicle coordinate system on the ground z-vector was Linear Acceleration (g) Linear Acceleration (A-pillar) 15 40

10 30

20 5 X 10 g g 0 Y M 1 1001 2001 3001 4001 5001 6001 0 -5 Z 1 1001 2001 3001 4001 5001 6001 -10

-10 -20

-15 -30 ms ms Buick Buick Linear Acceleration Linear Acceleration (A-pillar) 15 30

10 20

5 10

0 X g g 0 M 1 1001 2001 3001 4001 5001 6001 Y 1 1001 2001 3001 4001 5001 6001 -5 Z -10 -10 -20 -15 -30 -20 ms ms Oldsmobile Oldsmobile Linear Acceleration (A-pillar) Linear Acceleration 50 20 40

15 30 10 g 20 X M 5 10 g Y 0 0 1 1001 2001 3001 4001 5001 6001 Z 1 1001 2001 3001 4001 5001 6001 -5 -10 -10 -20 ms -15 ms Pontiac Pontiac Figure 14. Left A-pillar accelerometer data. Larger graphs Figure 12. Triaxial linear acceleration of the three are presented in Appendix C. vehicles. Larger graphs are presented in Appendix C.

Linear Acceleration Magnitude 16 14 12 10 g 8 M 6 4 2 0 1 1001 2001 3001 4001 5001 6001 ms Buick Linear Acceleration Magnitude 20 18 16 14 12 Figure 15. Oldsmobile test. Note the passenger side rear g 10 M 8 6 door opened and then shut (top rear in the 4 2 0 video sequence above). 1 1001 2001 3001 4001 5001 6001 ms Oldsmobile While reviewing the video, it was discovered that Linear Acceleration Magnitude 18 the passenger rear door on the Oldsmobile opened 16 14 12 and then slammed shut during the roll sequence g 10 8 M (Figure 15). At final rest, the door was latched 6 4 2 shut. 0 1 1001 2001 3001 4001 5001 6001 ms Pontiac DISCUSSION Figure 13. Magnitude (vector sum) of the linear While the test apparatus, test conditions and speed acceleration of the three vehicles. Larger at which the vehicles were launched were similar, graphs are presented in Appendix C. the resulting motion was significantly different, Single axis accelerometers were attached to the reflecting the chaotic nature of rollovers. This is right and left A-pillars; however, the left A-pillar consistent with the findings of Orlowski, et al. accelerometer failed. The data for the right A- (1985) and Bahling, et al. (1990) and the pillar was converted from voltage to g’s and observations of Moffatt, et al. (2003). filtered. Gravity was not, however, subtracted. The data is presented in Figure 14 for the three The average deceleration (effective drag) was vehicles . calculated and ranged from 0.34 to 0.54. This compares favorably with a range of 0.36 to 0.61 impact slowed the rotational velocity. The second reported by Orlowski, et al. (1989). It should be impact was relatively flat on the roof which noted that the distance used in calculating the stopped the vehicles motion. effective drag in these tests is from lift-off of the following tires from the upper portion of the sled Review of the test data showed similar angular ramp to final rest. Further, the vehicle started at a velocities as those reported by Orlowski, et al. position above the plane of the ground at a 34° (1985 and 1989). angle from horizontal. The vehicles, as they approached their final rest, In these four tests, the Pontiac tended to impact experienced a relatively flat (roof up or wheels up) the ground as the vehicle was coming up on its impact to the forward edge, producing an upward side, with the center of gravity more or less above force forward of the center of gravity. This the ground contact point. The principal direction resulted in a large retarding torque, effectively of force therefore tended to pass near or behind stopping the X-axis rotation. This can be seen in the center of gravity and therefore the motion had the angular velocity graphs shown in Appendix C. a barrel roll appearance for the first 3+ rolls. This The stopping torque apeared quite large on the resulted in the most number of rolls (4¼) , the Oldsmobile and Buick, as compared to the longest distance traveled (39.6m) and the lowest impacts on the Pontiac. The vehicles in general effective drag (0.34) for the four tests. During the showed some yaw during the last half roll, as final ¾ roll on the Pontiac, the vehicle yawed recorded in Table 3. approximately 35º clockwise (CW) as seen from above resulting in a wheel down impact with the Evidence of rollover impacts that are more side rear angled forward. That stopped most of the oriented, with the center of gravity above the motion, except a slow roll onto its left (driver’s) impact and with multiple rolls, may suggest a side. Interestingly, on the second ground impact, lower effective drag coefficient during the roll the rotational velocity for the Pontiac increased phase as compared with a heavy forward edge flat significantly from less than 5 to over 9 radians per impact with fewer rolls. This appears consistent second. At the end of the second roll, the anglular with the Malibu tests, Orlowski, et al. (1985) and velocity was approximately 6 radians per second. Bahling, et al. (1990), which also shows an It then slowed to approximately 4 radians per inverse relationship between number of rolls and second until the wheel impact at the end of the the average deceleration (effective drag fourth roll. coefficient), as shown in Table 5.

The Buick angular velocity barely reached 6 # rolls # tests Avg. distance (m) Avg. drag radians per second. At the end of the second roll, 2 1 19.8 0.67 the vehicle landed relatively hard on its wheels, 2 ½ 2 21.35 0.63 and the rotation was abruptly stopped. The Buick 3 4 23.63 0.57 experienced a very slight approximately 10º 3 ¼ 2 26.8 0.50 clockwise CW yaw in the last ½ roll. 3 ½ 6 25.58 0.52 The Oldsmobile achieved an angular velocity of 4 1 31.1 0.43 nearly 8 radians per second. During the last ½ Table 5. Combined data for Malibu tests showing average roll, the vehicle yawed approximately 70º counter deceleration (effective drag coefficient) appears clockwise (CCW) and landed on its tires, with the inversely related to number of rolls. rear forward, stopping the roll. The nine-accelerometer array was very effective The Mercury motion was analyzed using video in determining the rotational acceleration. The alone, because of the failure of the data collection error in rotational displacement after normalizing system. The Mercury had what appeared to be a the data and a double integration was 3 % or less heavy impact after approximately 1 revolution for the Pontiac and Buick. The Oldsmobile, which left tire rim gouges in the asphalt test which showed the largest bias in the angular surfaces and knocked off the hub caps. The first acceleration and velocity data, showed a displacement error on the order of 14%. The bias corrections used in the angular accleration and The angular roll velocity achieved by the Buick velocity calculations were small compared to the and Oldsmobile was approximately one revolution peaks in the uncorrected data, well below that per second. As mentioned earlier, the Pontiac’s which can be detected on the graphical angular roll velocity was approximately 1½ presentation of the data. The Oldsmobile was revolutions per second after the second ground tested between the Buick and the Pontiac, with the impact, but decreased to approximately 1 test equipment moved from vehicle to vehicle. revolution per second after the third ground Therefore, test equipment malfunction is unlikely. impact. It is important to note that the rotational acceleration is calculated by taking the difference The magnitude of the linear acceleration for the between two accelerometer readings, which for vehicles achieved a peak of approximately 14 to low levels of angular acceleration can produce a 19 g’s. These peaks were fairly narrow, large error as a percentage of the reading, while approximately 10-20 ms. both of the original readings are within specifications. The percentage error is Several areas can be improved in this test method. substantially reduced for higher differences. A rate sensor, to measure angular velocity is While the Oldsmobile had the greatest yaw during recommended in at least the X axis. Several video the final half revolution, it is not obvious why that cameras, with fixed markers in the background would affect the roll integration which is taken would improve the precision of the video about the X axis. While the source of the error photogrammetry and would be useful in could not be identified, it does not appear to be measuring the intitial speed of the vehicle as it due to failure of any of the equipment and begins to roll off the sled. therefore it is likely to be relatively small error which spans the entire period of the roll. Rollovers by nature are chaotic. Therefore, in Therefore, the peak values are likely good testing, as with actual rollover accidents, slight indications of the peak rotational accelerations changes can produce significantly different which the vehicle experienced. results. This apparatus does not attempt to control all of the variables and therefore is not appropriate It should be noted that angular rate (velocity) when repeatable results are to be achieved. sensors are available and are typically used in rollover testing. In this testing, angular velocities CONCLUSIONS of approximately 1½ rotations per second were The rollover tests demonstrate the chaotic nature seen, while many of the angular velocity sensors of rollover accidents and the difficulty in are linear to approximately 1 rotation per second. reconstruction. From this testing, as well as Further, rate sensors are not appropriate to previous work that examines X-axis rolls on a flat determine impact rotational and linear surface, an increase in the number of rolls tends to accelerations. Rate sensors would be an excellent result in greater travel distance and lower effective supplement to the 9-accelerometer array. drag factor. Nonetheless, double integration of the rotational acceleration data should be performed as a check These tests demonstrate a simple, portable and of the rotational acceleration data. inexpensive method of performing rollover tests with kinematic data. Additional video cameras, During the test of the Oldsmobile, its right rear with known background markers and at least an door opened and closed. Prior to the beginning of X-axis rate sensor would improve the quality of the test, the door was latched but unlocked and at the data collected. final rest the door was again latched. As can be seen in the photographs in Appendix B, the vehicle had experienced a lateral impact to the right rear quarter panel, but its relationship to the door opening, if any, is unknown.

ACKNOWLEDGMENTS Orlowski, K.F., Bundorf, R.F, and Moffatt, E.A., The authors wish to thank the Institute of Police “Rollover Crash Tests – The Influence of Roof Technology and Management, Mr. David Brill, Strength on Injury Mechanics”, SAE who coordinated the testing in conjuction with the International, SAE Paper 851734, Warringdale, annual IPTM Special Problems Conference and PA, 1985.

Mr. Gary Stephens, who provided the truck and Orlowski, K.F., Moffatt, E.A. Bundorf, R.F, and the financial support to construct the sled. Holcomb, M.P., “Reconstruction of Rollover Collisions”, SAE International, SAE Paper A special thank you to the AEGI staff, particularly 890857, Warringdale, PA, 1989. Susan Stevens and Brenda Scruggs for their astute editing of this paper. Padgaonkar, A.J., Kreiger, K.W., and King, A.I., “Measurement of Angular Acceleration of a Rigid REFERENCES Body Using Linear Accelerometers”, ASME, Journal of Applied Mechanics, 1975. Bahling, G.S., Bundorf, R.T., Kaspzyk, G.S., Moffatt, E.A., Orlowski, K.F., and Stocke, J.E., SAE J211-1 Recommended Practice “Rollover and Drop Tests – The Influence of Roof “Instrumentation for Impact Test – Part 1 – Strength on Injury Mechanics Using Belted Electronic Instrumentation”, SAE International, Dummies”, SAE International, SAE Paper Warringdale, PA. 902314, Warringdale, PA, 1990. SAE J2114 Recommended Practice “Dolly Mital, N.K., King, A.I., “Computation of Rigid- Rollover Recommended Test procedure”, SAE Body Rotation in Three-Dimensional Space from International, Warringdale, PA. Body-Fixed Linear Acceleration Measurements”, ASME, Journal of Biomechanical Engineering, 78-WA/Bio-5, American Society of Mechanical CONTACT Engineers, 1978. Orion P. Keifer Moffatt, E.A., Cooper, E.R., Cronteau, J.J., Applications Engineering Group, Inc. (AEGI) Orlowski, K.F., Marth, D.R., and Carter, J.W., 1200 Mayport Road “Matched-Pair Rollover Impacts of Rollcaged and Atlantic Beach, Florida 32233 Production Roof Cars Using the Controlled 800-777-7668 Rollover Impact System (CRIS)”, SAE paper [email protected] 2003-01-0172, SAE International, Warrendale, PA, 2003. Appendix A

INSTRUMENTATION

A computer system was assembled to collect data. The components included a VIA Motherboard 600MHz VIA C3 CPU, with integral ethernet, and 512 MB RAM, with a 12 volt power supply. The operating system was Windows 98 SE. Data was collected with a Data Translation 9800 USB A\D converter, using the included data software. Data was stored on a Sandisk Ultra 512 MB flash memory card. All data was collected with 12 bit resolution.

The accelerometers used are summarized in Table A-1. Power for the accelerometers was provided by a nine volt dry-cell battery through a five volt regulated power supply.

The monitored accelerometers included a nine-accelerometer array, as proposed by Padgaonkar, et al. (1975) and Mital and King (1979), including three mutually perpendicular channels on the center accelerometer and the two channels for each of the three legs. The leg accelerometers were triaxial, but only the two axes perpendicular to the axis of the leg were monitored, as shown in Figure A-1.

Figure A-1. Configuration of the nine-accelerometer array.

Linear acceleration in three directions are measured and used directly from the triaxial accelerometer at the origin of the array. Rotational accelerations are calculated by taking the difference between measured acceleration of two parallel accelerometer channels, divided by the perpendicular distance separating the accelerometer lines of action. As can be seen, angular acceleration about each of the axis can be calculated by using accelerometers on either of the other two axes. In this formulation, the two calculated angular accelerations are averaged. Mathematically from Mital and King (1979), equation 5:

ω xz1z0y1y3y0z3=(A-A)/2ρ -(A-A)/2ρ

ω yx3x0x3z2z0x2=(A-A)/2ρ -(A-A)/2ρ

ω zy2y0x2x1x0y1=(A-A)/2ρ -(A-A)/2ρ

Where: ω = angular acceleration A = measured acceleration ρ = distance between accelerometers (leg length)

Three channels of a 2g triaxial accelerometer, installed on the floor near the center of gravity, were monitored. Two single axial 50 g accelerometers were placed near the right and left A-pillar roof

Appendix A

INSTRUMENTATION intersection. The position and orientation, with respect to the vehicle coordinate axis varied from vehicle to vehicle, but in general were oriented mostly vertically with a forward and outboard component as dictated by the interior contour at the A-pillar to roof contour inside the vehicle.

Additionally, one data collection channel monitored a microphone, used for video to data collection synchronization and one channel monitored the five volt power supply for the accelerometers.

Position Range Manufact Model S/N A Center ± 25 g’s Crossbow CXL25LP3 0100927 r Leg 1 ± 25 g’s Crossbow CXL25LP3 0020972 r a Leg 2 ± 25 g’s Crossbow CXL25LP3 0100926 y Leg 3 ± 25 g’s Crossbow CXL25LP3 9915614 CG fixed ± 2 g’s Crossbow CXL02LP3 0019325 Left A Pillar ± 50 g’s Crossbow CXL50LP3 0100054 Right A Pillar ± 50 g’s Crossbow CXL50LP3 0023315 Table A-1. Accelerometer data and placement.

The nine-accelerometer array was attached to a steel frame with three mutually orthogonal legs. The frame was installed in the vehicles with the origin up as shown diagrammatically in Figure A- 2.

Figure A-2. Diagram of the nine-accelerometer array orientation in the test vehicles.

Appendix B Buick Photographs

Figure B-1. Figure B-2.

Figure B-3. Figure B-4.

Figure B-5. Figure B-6.

Appendix B

Oldsmobile Photographs

Figure B-7. Figure B-8.

Figure B-9. Figure B-10.

Figure B-11. Figure B-12.

Appendix B

Pontiac Photographs

Figure B-13. Figure B-14.

Figure B-15. Figure B-16.

Figure B-17. Figure B-18.

Appendix B

Mercury Photographs

Figure B-19. Figure B-20.

Figure B-21. Figure B-22.

Figure B-23. Figure B-24.

Appendix C

Buick Accelerometer Data

Angular Acceleration 150 100 50

2 X 0 1 1001 2001 3001 4001 5001 6001 Y rad/s -50 Z -100 -150 -200 ms

Angular Acceleration 150

100

50 2 0 1 1001 2001 3001 4001 5001 6001 rad/s -50 X

-100

-150

-200 ms

Appendix C

Buick Accelerometer Data

Angular Velocity 2 1 0 -1 1 1001 2001 3001 4001 5001 6001 X -2 rad/s -3 Y -4 Z -5 -6 -7 ms

Angular Velocity 2 1 0 -1 1 1001 2001 3001 4001 5001 6001 -2 X rad/s -3 -4 -5 -6 -7 ms

Appendix C

Buick Accelerometer Data

Angular Displacement 2 0 1 1001 2001 3001 4001 5001 6001 -2 -4 X

rad -6 Y -8 Z -10 -12 -14 ms

Linear Acceleration (g) 15

5 X g 0 Y 1 1001 2001 3001 4001 5001 6001 -5 Z

-10

-15 ms

Appendix C

Buick Accelerometer Data

Linear Acceleration Magnitude 16 14 12 10 g 8 M 6 4 2 0 1 1001 2001 3001 4001 5001 6001 ms

Linear Acceleration (A-pillar) 40 30

20 10 g 0 M 1 1001 2001 3001 4001 5001 6001 -10 -20 -30 ms

Appendix C

Oldsmobile Accelerometer Data

Angular Acceleration 150

100

50 X 0 Y

rad/s2 1 1001 2001 3001 4001 5001 6001 -50 Z

-100

-150 ms

Angular Acceleration 100

0 1 1001 2001 3001 4001 5001 6001 X rad/s2 -50

-100

-150 ms

Appendix C

Oldsmobile Accelerometer Data

Angular Velocity 10

4 X Y rad/s 2 Z 0 1 1001 2001 3001 4001 5001 6001 -2 -4 ms

Angular Velocity 9 8 7 6 5 4 X

rad/s 3 2 1 0 -1 1 1001 2001 3001 4001 5001 6001 -2 ms

Appendix C

Oldsmobile Accelerometer Data

Angular Displacement 16 14 12 10 8 X 6 rad Y 4 Z 2 0 -2 1 1001 2001 3001 4001 5001 6001 -4 ms

Linear Acceleration 15

0 X g 1 1001 2001 3001 4001 5001 6001 Y -5 Z -10

-15

-20 ms

Appendix C

Oldsmobile Accelerometer Data

Linear Acceleration Magnitude 20 18 16 14 12 g 10 8 M 6 4 2 0 1 1001 2001 3001 4001 5001 6001 ms

Linear Acceleration (A-pillar) 30

10 g 0 M 1 1001 2001 3001 4001 5001 6001 -10

-20

-30 ms

Appendix C

Pontiac Accelerometer Data

Angular Acceleration 150

100

50 2 X 0 Y rad/s 1 1001 2001 3001 4001 5001 6001 Z -50

-100

-150 ms

Angular Acceleration 150

100

50 2

0 X rad/s 1 1001 2001 3001 4001 5001 6001 -50

-100

-150 ms

Appendix C

Pontiac Accelerometer Data

Angular Velocity 2 0 1 1001 2001 3001 4001 5001 6001 -2 -4 X rad/s -6 Y Z -8 -10 -12 ms

Angular Velocity 0 1 1001 2001 3001 4001 5001 6001 -2

-4

-6 rad/s X -8

-10

-12 ms

Appendix C

Pontiac Accelerometer Data

Angular Displacement 5 0 1 1001 2001 3001 4001 5001 6001 -5 -10 X rad Y -15 Z -20

-25 -30 ms

Linear Acceleration 20 15 10 5 X g Y 0 1 1001 2001 3001 4001 5001 6001 Z -5 -10 -15 ms

Appendix C

Pontiac Accelerometer Data

Linear Acceleration Magnitude 18 16 14 12 10 g 8 M 6 4 2 0 1 1001 2001 3001 4001 5001 6001 ms

Linear Acceleration (A-pillar) 50 40 30 g 20 M 10

0 1 1001 2001 3001 4001 5001 6001 -10 -20 ms